The Official ACT Mathematics Guide

Master the math section of the ACT with the only official guide prepared by the creators and administrators of the test The Official ACT Mathematics Guide, 3rd Edition, is the most recent and authoritative update to the leading study resource for the widely used college admissions test. This comprehensive guide shows you what to expect on test day, offering intuitive and concept-based instruction, actual test questions from previous exams, and expert insights that reduce test anxiety and build confidence. This book reflects the most recent changes to the ACT mathematics section and delivers a complete review of every math concept tested. With both print and customizable online practice questions, students can prepare in the way they feel most comfortable while working through problems organized by question type. You’ll also find: Real ACT math questions from previous test administrations combined with detailed explanations for every problem A concept-based approach that helps students understand the mathematical topics they'll encounter on test day Comprehensive review of the entire mathematics section so students know exactly what to expect Online access to the complete question pool for personalized, customizable practice sessions Organization by question type to help students identify strengths and target areas needing improvement Ideal for high school students preparing for college admissions or scholarship qualification, The Official ACT Mathematics Guide is a detailed and authoritative resource designed to help students of all skill levels perform at their highest level on test day.

Introduction vii Chapter 1: The ACT Math Test 1 Reporting Categories: Score Reporting 2 Reporting Categories: Topic Overview 2 Chapter 2: Number and Quantity 5 Real Numbers 5 Number Line and Absolute Value 6 Exponents 17 Imaginary and Complex Numbers 22 Vectors 27 Matrices 30 Chapter 2: Quiz Answers 35 Chapter 3: Algebra 41 Scientific Notation 41 Equations 43 Linear Equations 51 System of Equations 53 Solving Systems of Equations Using Matrices 58 Roots 70 Logarithmic Equations 74 Chapter 3: Quiz Answers 75 Chapter 4: Functions 83 Domain and Range 83 Slope-Intercept Form of a Linear Equation 84 Slope and Intercept from a Line in the Coordinate Plane 86 Function Representation 88 Transformations of Functions 92 Inverse of a Function 95 Patterns and Modeling 98 Sequences 99 Unit Circle 102 Periodic Functions 106 Trigonometric Identities 110 Chapter 4: Quiz Answers 113 Chapter 5: Geometry 117 Coordinate Geometry 117 Lines and Angles 118 Two-Dimensional Shapes 121 Constructions and Proof 142 Three-Dimensional Shapes 145 Trigonometry 149 Chapter 5: Quiz Answers 155 Chapter 6: Statistics and Probability 161 Simple Probability 161 Sets of Numbers 166 Charts 170 Chapter 6: Quiz Answers 179 Chapter 7: Practice Questions 185 Chapter 8: Answers and Explanations 235 Answer Key and Explanatory Answers: Practice Test 1 236 Answer Key and Explanatory Answers: Practice Test 2 251 Answer Key and Explanatory Answers: Practice Test 3 263 Answer Key and Explanatory Answers: Practice Test 4 276